It is possible that Morggán participated in the so-called Revolt of the Earls, a protest by some of the native Scottish nobility during King Máel Coluim IV's trip to France as a vassal of King Henry II of England.
Agnes was probably related to the de Warenne family - the family who married Ada de Warenne to Henry of Scotland - and who was mother of Kings Malcolm IV and William the Lion.
Morggán and Agnes had at least one son, Donnchad, who eventually succeeded to become a Mormaer of Mar.
Morggán had another two sons, Máel Coluim and James, but they may have been illegitimate - that is, the product of an uncanonical marriage acceptable in the Celtic system, but not in the Franco-Roman system that was gaining favour in Scotland at the time.
His daughter Alesta of Mar was married to Alan Fitzwalter, 2nd High Steward of Scotland and was possibly mother to Walter Stewart, 3rd High Steward of Scotland.